Small time two-sided LIL behavior for Lévy processes at zero.

Authors :: Savov, Mladen
Source :: Probability Theory & Related Fields; May2009, Vol. 144 Issue 1/2, p79-98, 20p
Publication Year :: 2009
Abstract: We wish to characterize when a Lévy process X<subscript> t</subscript> crosses boundaries b( t), in a two-sided sense, for small times t, where b( t) satisfies very mild conditions. An integral test is furnished for computing the value of sup<subscript> t→0</subscript>| X<subscript> t</subscript>|/ b( t) = c. In some cases, we also specify a function b( t) in terms of the Lévy triplet, such that sup<subscript> t→0</subscript> | X<subscript> t</subscript>|/ b( t) = 1. [ABSTRACT FROM AUTHOR]